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2 years ago

Which is true regarding the graphed function f(x)?

Mathematics

1 answer:

Sladkaya [172]2 years ago

6 0

<h2>Explanation:</h2>

Hello! Remember you have to write complete questions in order to get good and exact answers. Here I'll assume the graphed function comes from:

$f(x)=\left(x-4\right)^{2}+5$

So this is the equation of a parabola that opens upward and whose vertex lies on the point:

$V(4,5)$

The graph of this function is shown below. Which is true regarding the graphed function f(x)?

It is true that the domain is the set of all real numbers because this is a polynomial function.

It is true that the range is the set of all real numbers such that y ≥ 5

It is true that this parabola opens upward

It is true that it doesn't cut the x-axis

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Maria has 90$ in a saving account.The interest rate rise a 5% compounded annually.to the nearest cent, how much will he have in

-Dominant- [34]

Answer:

$104.19

Step-by-step explanation:

We will use the compound interest formula to solve this:

$A=P(1+\frac{r}{n} )^{nt}$

<em>P = initial balance</em>

<em>r = interest rate (decimal)</em>

<em>n = number of times compounded annually</em>

<em />

First, lets change 5% into a decimal:

5% -> $\frac{5}{100}$ -> 0.05

Now, plug the values into the equation:

$A=90(1+\frac{0.05}{1})^{1(3)}$

$A=104.19$

After 3 years, Maria will have $104.19

8 0

2 years ago

HOW TO SOLVE 2/5x=-25

Pepsi [2]

Answer:

x = - $\frac{125}{2}$ = - 62.5

Step-by-step explanation:

Given

$\frac{2}{5}$ x = - 25

Multiply both sides by 5 to clear the fraction

2x = - 125 ( divide both sides by 2 )

x = - $\frac{125}{2}$ = - 62.5

6 0

2 years ago

Read 2 more answers

Which scenario does not represent exponential growth?

storchak [24]

Answer:

I believe the correct answer is - The value of a bank account with quarterly compounded interest after 6 years.

I'm not sure if this is 100% correct but hope it helps.

4 0

2 years ago

HELP WITH NUMBER 13 please

amid [387]

Answer: QE = 10

Step-by-step explanation: To solve this problem, it's important to understand that the diagonals of a parallelogram bisect each other.

This means that E is the midpoint of diagonal SQ.

So we can setup the equation x² + 9x = 4x + 6.

To solve this polynomial equation, set it equal to zero first.

So we have x² + 5x - 6 = 0 and we get (x + 6)(x - 1) = 0

when we factor the left side of the equation.

So this means that x = -6 or x = 1.

However, -6 will give us a negative length when we plug it in

to find QE so this will not work.

However, plugging 1 in will give us 10 as a length so QE = 10.

4 0

2 years ago

Use lagrange multipliers to find the shortest distance, d, from the point (4, 0, −5 to the plane x y z = 1

Varvara68 [4.7K]

I assume there are some plus signs that aren't rendering for some reason, so that the plane should be $x+y+z=1$ .

You're minimizing $d(x,y,z)=\sqrt{(x-4)^2+y^2+(z+5)^2}$ subject to the constraint $f(x,y,z)=x+y+z=1$ . Note that $d(x,y,z)$ and $d(x,y,z)^2$ attain their extrema at the same values of $x,y,z$ , so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.

The Lagrangian is

$L(x,y,z,\lambda)=(x-4)^2+y^2+(z+5)^2+\lambda(x+y+z-1)$

Take your partial derivatives and set them equal to 0:

$\begin{cases}\dfrac{\partial L}{\partial x}=2(x-4)+\lambda=0\\\\\dfrac{\partial L}{\partial y}=2y+\lambda=0\\\\\dfrac{\partial L}{\partial z}=2(z+5)+\lambda=0\\\\\dfrac{\partial L}{\partial\lambda}=x+y+z-1=0\end{cases}\implies\begin{cases}2x+\lambda=8\\2y+\lambda=0\\2z+\lambda=-10\\x+y+z=1\end{cases}$

Adding the first three equations together yields

$2x+2y+2z+3\lambda=2(x+y+z)+3\lambda=2+3\lambda=-2\implies \lambda=-\dfrac43$

and plugging this into the first three equations, you find a critical point at $(x,y,z)=\left(\dfrac{14}3,\dfrac23,-\dfrac{13}3\right)$ .

The squared distance is then $d\left(\dfrac{14}3,\dfrac23,-\dfrac{13}3\right)^2=\dfrac43$ , which means the shortest distance must be $\sqrt{\dfrac43}=\dfrac2{\sqrt3}$ .

7 0

3 years ago